Problem: Find the greatest common factor of $44, 12,$ and $28$.
The greatest common factor (GCF) is the largest number that is a factor of $44, 12,$ and $28$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}44 &=2\cdot2\cdot11\\\\\\\\ 12&=2\cdot2\cdot3\\\\\\\\ 28&=2\cdot2\cdot7 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}44 &=2\cdot2\cdot11\\\\\\\\ 12&=2\cdot2\cdot3\\\\\\\\ 28&=2\cdot2\cdot7 \end{aligned}$ Each number shares the factors ${2}$ and $2,$ so the GCF is $2\cdot2={4}$. The greatest common factor of $44, 12,$ and $28$ is $4$.